数学最新文献

{"title":"Helmholtz quasi-resonances are unstable under most single-signed perturbations of the wave speed","authors":"Euan A. Spence ,&nbsp;Jared Wunsch ,&nbsp;Yuzhou Zou","doi":"10.1016/j.jde.2025.113441","DOIUrl":"10.1016/j.jde.2025.113441","url":null,"abstract":"<div><div>We consider Helmholtz problems with a perturbed wave speed, where the single-signed perturbation is linear in a parameter <em>z</em>. Both the wave speed and the perturbation are allowed to be discontinuous (modelling a penetrable obstacle). We show that there exists a polynomial function of frequency such that, for any frequency, for most values of <em>z</em>, the norm of the solution operator is bounded by that function.</div><div>This solution-operator bound is most interesting for Helmholtz problems with strong trapping; recall that here there exists a sequence of real frequencies, tending to infinity, through which the solution operator grows superalgebraically, with these frequencies often called <em>quasi-resonances</em>. The result of this paper then shows that, at every fixed frequency in the quasi-resonance, the norm of the solution operator becomes much smaller for most single-signed perturbations of the wave speed, i.e., quasi-resonances are unstable under most such perturbations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"440 ","pages":"Article 113441"},"PeriodicalIF":2.4,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144138250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Interval maps mimicking circle rotations","authors":"Jakub Bielawski ,&nbsp;Thiparat Chotibut ,&nbsp;Fryderyk Falniowski ,&nbsp;Michał Misiurewicz ,&nbsp;Georgios Piliouras","doi":"10.1016/j.cnsns.2025.108963","DOIUrl":"10.1016/j.cnsns.2025.108963","url":null,"abstract":"<div><div>We investigate the dynamics of maps of the real line whose behavior on an invariant interval is close to a rational rotation on the circle. We concentrate on a specific two-parameter family, describing the dynamics arising from models in game theory, mathematical biology and machine learning. If one parameter is a rational number, <span><math><mrow><mi>k</mi><mo>/</mo><mi>n</mi></mrow></math></span>, with <span><math><mrow><mi>k</mi><mo>,</mo><mi>n</mi></mrow></math></span> coprime, and the second one is large enough, we prove that there is a periodic orbit of period <span><math><mi>n</mi></math></span>. It behaves like an orbit of the circle rotation by an angle <span><math><mrow><mn>2</mn><mi>π</mi><mi>k</mi><mo>/</mo><mi>n</mi></mrow></math></span> and attracts trajectories of Lebesgue almost all starting points. We also discover numerically other interesting phenomena. While we do not give rigorous proofs for them, we provide convincing explanations.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"150 ","pages":"Article 108963"},"PeriodicalIF":3.4,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144168099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Takagi–van der Waerden functions in metric spaces and their Lipschitz derivatives","authors":"Oleksandr V. Maslyuchenko ,&nbsp;Ziemowit M. Wójcicki","doi":"10.1016/j.jmaa.2025.129726","DOIUrl":"10.1016/j.jmaa.2025.129726","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We introduce the Takagi–van der Waerden function with parameters &lt;span&gt;&lt;math&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; by setting &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;munderover&gt;&lt;mo&gt;∑&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/munderover&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is a maximal &lt;span&gt;&lt;math&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/span&gt;-separated set in a metric space &lt;em&gt;X&lt;/em&gt;. So, if &lt;span&gt;&lt;math&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; then &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is the Takagi function and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is the van der Waerden function which are well-known examples of nowhere differentiable functions. Then we prove that the big Lipschitz derivative &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Lip&lt;/mi&gt;&lt;/mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; if &lt;span&gt;&lt;math&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; and &lt;em&gt;x&lt;/em&gt; is a non-isolated point of &lt;em&gt;X&lt;/em&gt;. Moreover, if the shell porosity &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; for some &lt;em&gt;λ&lt;/em&gt; and each non-isolated point &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; then the little Lipschitz derivative &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;lip&lt;/mi&gt;&lt;/mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; for large enough &lt;span&gt;&lt;math&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and any non-isolated point &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. In particular, this is true for any normed space. Finally, we prove that for any open set &lt;em&gt;A&lt;/em&gt; in a metric (normed) space &lt;em&gt;X&lt;/em&gt; without isolated points there exists a continuous function &lt;em&gt;f&lt;/em&gt; such that &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Lip&lt;/mi&gt;&lt;/mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; (and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;lip&lt;/mi&gt;&lt;/mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129726"},"PeriodicalIF":1.2,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144170510","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence of a weak solution to the Yamabe type flow","authors":"Sitao Zhang","doi":"10.1016/j.nonrwa.2025.104418","DOIUrl":"10.1016/j.nonrwa.2025.104418","url":null,"abstract":"<div><div>In this paper, we study a doubly nonlinear parabolic equation, which is the Yamabe type heat flow on a bounded regular domain in Euclidean space. We show that under suitable assumptions on the initial data <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> one has a weak approximate discrete Morse flow for the Yamabe type heat flow on any time interval. We show the existence of a weak solution to the Yamabe type heat flow.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104418"},"PeriodicalIF":1.8,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144154677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Turán problems for star-path forests in hypergraphs","authors":"Junpeng Zhou ,&nbsp;Xiying Yuan","doi":"10.1016/j.disc.2025.114592","DOIUrl":"10.1016/j.disc.2025.114592","url":null,"abstract":"<div><div>An <em>r</em>-uniform hypergraph (<em>r</em>-graph for short) is linear if any two edges intersect at most one vertex. Let <span><math><mi>F</mi></math></span> be a given family of <em>r</em>-graphs. An <em>r</em>-graph <em>H</em> is called <span><math><mi>F</mi></math></span>-free if <em>H</em> does not contain any member of <span><math><mi>F</mi></math></span> as a subgraph. The Turán number of <span><math><mi>F</mi></math></span> is the maximum number of edges in any <span><math><mi>F</mi></math></span>-free <em>r</em>-graph on <em>n</em> vertices, and the linear Turán number of <span><math><mi>F</mi></math></span> is defined as the Turán number of <span><math><mi>F</mi></math></span> in linear host hypergraphs. An <em>r</em>-uniform linear path <span><math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ℓ</mi></mrow><mrow><mi>r</mi></mrow></msubsup></math></span> of length <em>ℓ</em> is an <em>r</em>-graph with edges <span><math><msub><mrow><mi>e</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>e</mi></mrow><mrow><mi>ℓ</mi></mrow></msub></math></span> such that <span><math><mo>|</mo><mi>V</mi><mo>(</mo><msub><mrow><mi>e</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo><mo>∩</mo><mi>V</mi><mo>(</mo><msub><mrow><mi>e</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>)</mo><mo>|</mo><mo>=</mo><mn>1</mn></math></span> if <span><math><mo>|</mo><mi>i</mi><mo>−</mo><mi>j</mi><mo>|</mo><mo>=</mo><mn>1</mn></math></span>, and <span><math><mi>V</mi><mo>(</mo><msub><mrow><mi>e</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo><mo>∩</mo><mi>V</mi><mo>(</mo><msub><mrow><mi>e</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>)</mo><mo>=</mo><mo>∅</mo></math></span> for <span><math><mi>i</mi><mo>≠</mo><mi>j</mi></math></span> otherwise. Gyárfás et al. (2022) <span><span>[9]</span></span> obtained an upper bound for the linear Turán number of <span><math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ℓ</mi></mrow><mrow><mn>3</mn></mrow></msubsup></math></span>. In this paper, an upper bound for the linear Turán number of <span><math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ℓ</mi></mrow><mrow><mi>r</mi></mrow></msubsup></math></span> is obtained, which generalizes the known result of <span><math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ℓ</mi></mrow><mrow><mn>3</mn></mrow></msubsup></math></span> to any <span><math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ℓ</mi></mrow><mrow><mi>r</mi></mrow></msubsup></math></span>. Furthermore, some results for the linear Turán number and Turán number of several linear star-path forests are obtained.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 11","pages":"Article 114592"},"PeriodicalIF":0.7,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144137779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Truncated Euler–Maruyama method for hybrid stochastic functional differential equations with infinite time delay","authors":"Jingchao Zhou,&nbsp;Henglei Xu,&nbsp;Xuerong Mao","doi":"10.1016/j.cam.2025.116773","DOIUrl":"10.1016/j.cam.2025.116773","url":null,"abstract":"<div><div>Li et al. (2023) developed a new theory to approximate the solution of hybrid stochastic functional differential equations (SFDEs) with infinite time delay via the numerical solution of the corresponding hybrid SFDEs with finite time delay. But hybrid SFDEs were required to be globally Lipschitz continuous. In this paper, we will lift this restriction. Under the local Lipschitz condition and the Khasminskii-type condition, numerical solutions of hybrid SFDEs with infinite time delay will be designed by using the truncated Euler–Maruyama method. The strong convergence and convergence rate of the numerical solutions in <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup><mrow><mo>(</mo><mi>q</mi><mo>≥</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> will be obtained. Finally, an example to stochastic functional volatility model is given to demonstrate the effectiveness of our new theory.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"472 ","pages":"Article 116773"},"PeriodicalIF":2.1,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144168355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local randomized neural networks with discontinuous Galerkin methods for KdV-type and Burgers equations","authors":"Jingbo Sun,&nbsp;Fei Wang","doi":"10.1016/j.cnsns.2025.108957","DOIUrl":"10.1016/j.cnsns.2025.108957","url":null,"abstract":"<div><div>The Local Randomized Neural Networks with Discontinuous Galerkin (LRNN-DG) methods, introduced in Sun et al. (2024), were originally designed for solving linear partial differential equations. In this paper, we extend the LRNN-DG methods to solve nonlinear PDEs, specifically the Korteweg–de Vries (KdV) equation and the Burgers equation, utilizing a space–time approach. Additionally, we introduce adaptive domain decomposition and a characteristic direction approach to enhance the efficiency of the proposed methods. Numerical experiments demonstrate that the proposed methods achieve high accuracy with fewer degrees of freedom, additionally, adaptive domain decomposition and a characteristic direction approach significantly improve computational efficiency.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"150 ","pages":"Article 108957"},"PeriodicalIF":3.4,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144168097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Accelerated failure time model under dependent truncated data","authors":"Jin-Jian Hsieh,&nbsp;Siang-Ying Chen","doi":"10.1016/j.jspi.2025.106297","DOIUrl":"10.1016/j.jspi.2025.106297","url":null,"abstract":"<div><div>This paper delves into the accelerated failure time model within the framework of dependent truncation data and leverages the copula model to establish correlations within the dataset. Building upon the work of Chaieb et al. (2006), who utilized the copula-graphic method to estimate survival functions and proposed an approach for estimating correlation parameters, we further extend the methodology by introducing two distinct estimation techniques for regression parameters. The first method involves parameter evaluation through the calculation of the area between survival curves, while the second method employs the weight of survival jump in conjunction with the least squares approach to estimate regression parameters. We evaluate the efficacy of these proposed estimation procedures through simulation studies and conduct a comparative analysis between the two approaches. Furthermore, we apply these methodologies to two real-world datasets, providing insights into their practical applicability. Through this analysis, we gain a deeper understanding of how these approaches can be effectively utilized in real-world scenarios.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"240 ","pages":"Article 106297"},"PeriodicalIF":0.8,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144166460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Algebro-geometric initial value problems for integrable nonlinear lattices: Tetragonal curves and Riemann theta function solutions","authors":"Xianguo Geng,&nbsp;Minxin Jia,&nbsp;Ruomeng Li","doi":"10.1016/j.geomphys.2025.105541","DOIUrl":"10.1016/j.geomphys.2025.105541","url":null,"abstract":"<div><div>In this paper, we establish the theory of tetragonal curves and address a series of fundamental problems within this framework, including the construction of a basis for holomorphic Abelian differentials, Abelian differentials of the second and third kinds, Baker-Akhiezer functions, and meromorphic functions. Building on these results, we apply the theory of tetragonal curves to investigate algebro-geometric initial value problems for integrable nonlinear lattice systems. As an illustrative example, we employ the discrete zero-curvature equation and the discrete Lenard equation to derive a hierarchy of coupled Bogoyavlensky lattice equations associated with a discrete <span><math><mn>4</mn><mo>×</mo><mn>4</mn></math></span> matrix spectral problem. By analyzing the characteristic polynomial of the Lax matrix for this hierarchy, we introduce a tetragonal curve and its associated Riemann theta function, exploring the algebro-geometric properties of Baker-Akhiezer functions and a class of meromorphic functions. Using the Abel map and Abelian differentials, we precisely straighten out various flows. Finally, we obtain Riemann theta function solutions for the algebro-geometric initial value problems of the entire coupled Bogoyavlensky lattice hierarchy.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"215 ","pages":"Article 105541"},"PeriodicalIF":1.6,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144169540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Forest cuts in sparse graphs","authors":"Vsevolod Chernyshev ,&nbsp;Johannes Rauch ,&nbsp;Dieter Rautenbach","doi":"10.1016/j.disc.2025.114594","DOIUrl":"10.1016/j.disc.2025.114594","url":null,"abstract":"<div><div>We consider the conjecture that every graph <em>G</em> of order <em>n</em> with less than <span><math><mn>3</mn><mi>n</mi><mo>−</mo><mn>6</mn></math></span> edges has a vertex cut that induces a forest. Maximal planar graphs do not have such vertex cuts and show that the density condition would be best possible. We verify the conjecture for planar graphs and show that every graph <em>G</em> of order <em>n</em> with less than <span><math><mfrac><mrow><mn>11</mn></mrow><mrow><mn>5</mn></mrow></mfrac><mi>n</mi><mo>−</mo><mfrac><mrow><mn>18</mn></mrow><mrow><mn>5</mn></mrow></mfrac></math></span> edges has a vertex cut that induces a forest.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 11","pages":"Article 114594"},"PeriodicalIF":0.7,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144137780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}